UN officials said Norway, Nigeria, Tanzania and Bangladesh are the first countries to offer troops.
Nigeria and Tanzania already have troops in the AU force, but said they were prepared to increase their contingent.
Jean-Marie Guehenno, the UN under secretary general for peacekeeping operations, confirmed one European country and some developing countries had offered battalions for a UN force.
Though there is no firm agreement on a creating a force, Guehenno said the pledges were made because "we do have interest in the mission and we want to keep up that interest."
At a meeting of potential contributors to the force, countries were warned of problems that could face any peacekeeping force.
Militants remain opposed to a Darfur peace agreement and in April Osama bin Laden, al-Qaeda's leader, has called on Muslims to resist "crusader" western forces in Darfur.
The UN Security Council passed a resolution in August calling for a UN force to take over from the ill-equipped African Union (AU) force in Darfur.
There are currently about 7,000 AU troops in the region but the organisation will increase troop numbers to 11,000 by the end of the year, after an extension in its mandate until December 31.
Sudan has strongly objected to the United Nations taking over from the AU.
At least 200,000 people have died since the war broke out in February 2002, according to UN estimates.
Guehenno has set a target of a UN force of more than 17,000 troops and 3,300 police to keep the peace and investigate allegations of atrocities in Darfur.
Condoleezza Rice, US secretary of state, said last Friday that "time is running out" to prevent an all-out Sudanese government onslaught against Darfur militants.
"The violence in Darfur must end, and it must end now," she told a special ministerial meeting of two dozen nations, plus the European Union and the United Nations in New York.
The meeting discussed sending a delegation to Khartoum in a further attempt to persuade Omar al-Beshir, the Sudanese president, to drop his opposition to deployment of the UN force.
Al-Beshir told the UN General Assembly last week that the UN force was part of a "Zionist" plot to "dismember" his country and "plunder" the country's natural resources.